CN107356417A - A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy - Google Patents

A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy Download PDF

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CN107356417A
CN107356417A CN201710523506.4A CN201710523506A CN107356417A CN 107356417 A CN107356417 A CN 107356417A CN 201710523506 A CN201710523506 A CN 201710523506A CN 107356417 A CN107356417 A CN 107356417A
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余岭
罗文峰
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Jinan University
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
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Abstract

The invention discloses a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy, comprise the following steps：1) multiple acceleration transducers are arranged in bolted joint structure to survey the acceleration responsive sequence of corresponding measuring point；2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, using standard deviation maximum as normalized parameter, normalize actual measureed value of acceleration response, the characteristics of being responded according to actual measureed value of acceleration selects suitable time series models to carry out data fitting in AR models, arma modeling and MA models；3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, using residual sequence standard deviation as structural response feature；4) relation that comentropy quantifies the residual sequence standard deviation of adjacent two measuring point is introduced, the structural damage sensitive indicator under state to be measured is calculated, identifies the damage of bolted joint structure.This method can accurately identify joint portion faulted condition, meet the requirement to the monitoring of bolted joint connection status.

Description

A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy
Technical field
The present invention relates to monitoring structural health conditions field, and in particular to a kind of fusion Time-Series analysis is combined with the bolt of comentropy Portion's damnification recognition method.
Background technology
For engineering structure health monitoring system, the monitoring of bolted joint connection status is extremely important, and it is connection The key component of load is transmitted between part, affects the safe for operation of structure.However, because the bolted joint mechanism of action is complicated, By nonlinear theory or linear theory come to describe the true mechanical behavior of joint portion be extremely difficult, and model expend compared with High cost.In this context, the model-free methods for studying bolted joint non-destructive tests just seem particularly significant.The nothing being previously mentioned Model method refers to：Joint portion mechanical model need not be established, structural response signal is obtained by the sensor in structure, And architectural feature is extracted from structural response, the damage of identification joint portion.
At present, bolted joint Study on Damage Identification has been achieved with many achievements, be broadly divided into " having model method " with " model-free methods ".Entitled " a kind of spatial mesh structure node bolt loosens the diagnostic method of damage ", patent application Number be 201310006366.5 Chinese invention patent, by obtain bolt ball connect moment of flexure-rotation curve, will connection make With being equivalent to straight-bar.[Li Ling, Cai Anjiang, Cai Ligang, Guo Tieneng, the Ruan Xiaoguang bolted joint dynamic characteristics identification side such as Li Ling Method [J] mechanical engineering journals, 2013,49 (7):168-175.] from macroscopic aspect, joint portion connection function is expressed as The spring connection of limited individual point, obtains the equivalent linear model of bolted joint on joint face.The mechanics of connector interaction Model is complicated, and influence factor is numerous, it is difficult to the accurate mechanical model of joint portion is established from constitutive relation aspect.Modeling is complicated, no Accurately so that there is model method to expend higher cost during bolted joint non-destructive tests, and model error reduces The reliability of non-destructive tests result.
Model-free methods need not establish joint portion model, directly judge joint portion state by structural response feature, keep away Model error is exempted from.There are mapping relations in configuration state, theoretical based on time series analysis with its response sequence data rule, from The rule of autocorrelation angles analyze data, its statistical nature is obtained, so as to identify structural damage.Time Series Analysis Method only needs to measure Structure time response series, measurement are easily achieved, and are easy to apply.Conventional analysis model has AR models, MA models, arma modeling Deng.The key for accurately identifying joint portion damage is to build the damage locating index that can truly reflect structural damage situation (Damage sensitive feature,DSF).Someone is with the AR model residual sequence standards under state to be measured and normal condition The ratio between difference is damage locating index, and also someone is damaged using higher order statistical square (the kurtosis, the degree of bias) structure of AR model residual sequences Sensitive indicator.The structure thought of existing index is typically to investigate the degree that structure condition responsive to be measured deviates normal condition, but nothing Configuration state can be caused to deviate normal condition, thus easily erroneous judgement joint portion damage by connector damage or joint portion damage.
The content of the invention
The purpose of the present invention is to be directed to above-mentioned the deficiencies in the prior art, there is provided a kind of Time-Series analysis and comentropy of merging Bolted joint damnification recognition method, this method need not establish joint portion mechanical model, merely with the acceleration responsive of structure Time-histories sequence just can complete joint portion non-destructive tests, and methods described damages sensitivity to joint portion, can accurately identify joint portion Damage, meet the requirement to the monitoring of bolted joint connection status.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy, methods described include following step Suddenly：
1) arrange that exciting bank is used to give structure white-noise excitation, while the cloth in structure in bolted joint structure Put the acceleration responsive sequence that multiple acceleration transducers are used for surveying structurally corresponding measuring point；
2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, is joined by normalization of standard deviation maximum The characteristics of number, normalizing actual measureed value of acceleration response, being responded according to actual measureed value of acceleration is selected in AR models, arma modeling and MA models Select suitable time series models and carry out data fitting；
3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, using residual sequence standard deviation as knot Structure response characteristic；
4) relation for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, is calculated under state to be measured Structural damage sensitive indicator, identify bolted joint structure damage.
Further, in step 1), the multiple acceleration transducer is arranged in each connector of bolted joint structure Both sides.
Further, the bolted joint damnification recognition method of a kind of fusion Time-Series analysis and comentropy specifically includes Following steps：N number of measuring point is arranged altogether in each connector both sides of bolted joint structure, and white noise is measured by acceleration transducer Acceleration responsive sequence { the x of measuring point is corresponded under acoustically-driveni, sequence { xiRepresent that measuring point i is gathered under same time separation delta t N acceleration responsive sequences in order, the acceleration responsive sequence initial data maximum standard deviation max gathered with N number of measuring point (σi) it is normalized parameter, carry out data normalization：
In formulaIt is measuring point i acceleration responsive sequences { xiAverage,It is measuring point i original in t acceleration responsive Data xi,tValue after normalization, calculate the auto-correlation coefficient and partial correlation coefficient of each measuring point：
In formulaIt is acceleration responsive values of the measuring point i in t+k time Δts, ρi(k) measuring point i k rank auto-correlations system is represented Number, measuring point i k ranks partial correlation coefficient is equal with the value of k-th of autoregressive coefficient of AR (k) models, can be in MATLAB instruments Obtained after AR (k) model parameters of case estimation response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, select AR moulds Suitable time series models carry out data fitting in type, arma modeling or MA models：
In formulaAcceleration responsive values of the measuring point i in t- time Δts, measuring point i are represented respectively T-2 time Δts acceleration responsive value ... measuring point i in the acceleration responsive value of t-p time Δts, εt、εt-1……εt-qPoint Not Biao Shi the residual error of t, t- time Δts residual error ... t-q time Δts residual error,Is represented respectively One autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnFirst cunning is represented respectively Dynamic regression coefficient, second slip regression coefficient ..., n-th of slip regression coefficient, subscript p, q represent to include p in model respectively Rank autoregressive coefficient and q ranks slide regression coefficient；After selecting suitable time series models, complete to join using MATLAB tool boxes Number estimation, during parameter Estimation, first setting models exponent number, using posteriority method, consider fitting degree and from becoming using BIC criterion Number is measured, an optimal models is selected in numerous valid models：
N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms state to be measured And each measuring point data of normal condition optimal models and estimate its parameter, calculate each measuring point actual measureed value of acceleration response data with Residual sequence between model of fit：
Residual sequence using between each measuring point actual measureed value of acceleration response data and model of fit is used as each Measuring Point Structure Response characteristic, introduces the relation that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, and the structural damage of structure is sensitive Index is the absolute value sum of the comentropy subitem difference of state to be measured and normal condition：
Ui=-pi log pi
σ in formulai(ε) and σi+1(ε) represents measuring point i and measuring point i+1 acceleration responsive residual sequence standard deviation, U respectivelyiTable Show by the comentropy subitem value of measuring point i and measuring point i+1 structures, wherein Uj testAnd Uj refState and normal condition to be measured are represented respectively Comentropy subitem, DSF (i) represent by measuring point i and measuring point i+1 acceleration responsive data calculate damage locating index value, If state to be measured comes self-structure normal condition, two adjacent measuring point response residual sequence standard deviations of state and normal condition to be measured The comentropy subitem of composition is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, bolt Joint portion region DSF (i) changes are much larger than other regional changes, so as to identify that bolted joint is damaged.
Further, if the auto-correlation coefficient hangover of each measuring point, partial correlation coefficient truncation then select AR models；It is if each The auto-correlation coefficient truncation of measuring point, partial correlation coefficient hangover then select MA models；If the auto-correlation coefficient hangover of each measuring point, partially Coefficient correlation hangover then selects arma modeling.
Further, a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy, during utilization Between series analysis model fitting white-noise excitation under bolted joint structure acceleration responsive data, by introducing comentropy amount Change the relation between the two neighboring measuring point of bolted joint structure, with state to be measured and the comentropy of normal condition acceleration responsive The absolute value sum for difference of itemizing is as damage locating index.
The present invention compared with prior art, has the following advantages that and beneficial effect：
The present invention has merged that Time-Series analysis is theoretical and information entropy theory, it is proposed that a kind of Time-Series analysis and comentropy of merging Bolted joint damnification recognition method, this method need not establish joint portion mechanical model, merely with the acceleration responsive of structure Time-histories sequence just can complete the non-destructive tests of joint portion, and methods described damages sensitivity to joint portion, can accurately identify joint portion damage Wound, meet the requirement to the monitoring of bolted joint connection status.
Brief description of the drawings
Fig. 1 is a kind of reality for the bolted joint damnification recognition method for merging Time-Series analysis and comentropy of the embodiment of the present invention Alms giver's flow chart.
Fig. 2 is the experimental provision sketch of the embodiment of the present invention.
Fig. 3 (a) is that the damage of free beam of the embodiment of the present invention sets sketch, and Fig. 3 (b) damages for cantilever beam of the embodiment of the present invention Sketch is set.
Fig. 4 is the specific recognition result figure of the embodiment of the present invention.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are unlimited In this.
Embodiment：
A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy is present embodiments provided, implements master Flow chart is as shown in figure 1, comprise the following steps：
1) arrange that exciting bank is used to give structure white-noise excitation, while the cloth in structure in bolted joint structure Put the acceleration responsive sequence that multiple acceleration transducers are used for surveying structurally corresponding measuring point；
2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, is joined by normalization of standard deviation maximum The characteristics of number, normalizing actual measureed value of acceleration response, being responded according to actual measureed value of acceleration is selected in AR models, arma modeling and MA models Select suitable time series models and carry out data fitting；
3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, using residual sequence standard deviation as knot Structure response characteristic；
4) relation for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, is calculated under state to be measured Structural damage sensitive indicator, identify bolted joint structure damage.
Specifically include following steps：N number of measuring point is arranged altogether in each connector both sides of bolted joint structure, passes through acceleration Acceleration responsive sequence { the x of measuring point is corresponded under degree sensor measurement white-noise excitationi, sequence { xiRepresent measuring point i when identical Between gather under separation delta t n acceleration responsive sequences in order, the acceleration responsive sequence initial data gathered with N number of measuring point Maximum standard deviation max (σi) it is normalized parameter, carry out data normalization：
In formulaIt is measuring point i acceleration responsive sequences { xiAverage,It is measuring point i original in t acceleration responsive Data xitValue after normalization, calculate the auto-correlation coefficient and partial correlation coefficient of each measuring point：
In formulaIt is acceleration responsive values of the measuring point i in t+k time Δts, ρi(k) measuring point i k rank auto-correlations system is represented Number, measuring point i k ranks partial correlation coefficient is equal with the value of k-th of autoregressive coefficient of AR (k) models, can be in MATLAB instruments Obtained after AR (k) model parameters of case estimation response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, if each survey The auto-correlation coefficient hangover of point, partial correlation coefficient truncation then select AR models；If the auto-correlation coefficient truncation of each measuring point, inclined phase The hangover of relation number then selects MA models；If the auto-correlation coefficient hangover of each measuring point, partial correlation coefficient hangover then select ARMA moulds Type.Suitable time series models in AR models, arma modeling or MA models are selected to carry out data fitting：
In formulaAcceleration responsive values of the measuring point i in t- time Δts, measuring point i are represented respectively T-2 time Δts acceleration responsive value ... measuring point i in the acceleration responsive value of t-p time Δts, εt、εt-1……εt-qPoint Not Biao Shi the residual error of t, t- time Δts residual error ... t-q time Δts residual error,Is represented respectively One autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnFirst cunning is represented respectively Dynamic regression coefficient, second slip regression coefficient ..., n-th of slip regression coefficient, subscript p, q represent to include p in model respectively Rank autoregressive coefficient and q ranks slide regression coefficient；After selecting suitable time series models, complete to join using MATLAB tool boxes Number estimation, during parameter Estimation, first setting models exponent number, using posteriority method, consider fitting degree and from becoming using BIC criterion Number is measured, an optimal models is selected in numerous valid models：
N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms state to be measured And each measuring point data of normal condition optimal models and estimate its parameter, calculate each measuring point actual measureed value of acceleration response data with Residual sequence between model of fit：
Residual sequence using between each measuring point actual measureed value of acceleration response data and model of fit is used as each Measuring Point Structure Response characteristic, introduces the relation that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, and the structural damage of structure is sensitive Index is the absolute value sum of the comentropy subitem difference of state to be measured and normal condition：
Ui=-pi log pi
σ in formulai(ε) and σi+1(ε) represents measuring point i and measuring point i+1 acceleration responsive residual sequence standard deviation, U respectivelyiTable Show by the comentropy subitem value of measuring point i and measuring point i+1 structures, wherein Uj testAnd Uj refState and normal condition to be measured are represented respectively Comentropy subitem, DSF (i) represent by measuring point i and measuring point i+1 acceleration responsive data calculate damage locating index value, If state to be measured comes self-structure normal condition, two adjacent measuring point response residual sequence standard deviations of state and normal condition to be measured The comentropy subitem of composition is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, bolt Joint portion region DSF (i) changes are much larger than other regional changes, so as to identify that bolted joint is damaged.
The bolted joint structure that the present embodiment form using cantilever beam and free beam as object, damage by description bolted joint Identification process, for experimental provision sketch as shown in Fig. 2 experiment cantilever beam length is 800mm, sectional dimension is 50mm × 10mm；From It is 400mm by beam length, sectional dimension is 50mm × 10mm；Material is steel；Contact length is 50mm, and connecting bolt is M14 plain bolts.Bolted joint non-destructive tests specific implementation step is as follows：
(1) excitation and response measuring device are installed in bolted joint structure, exciting bank is exciting in the present embodiment Device, response measuring device are acceleration transducer, provide white-noise excitation by vibrator, 7 acceleration are arranged in structure Sensor (P1, P2……P7, as shown in Figure 2), structure is divided into 6 region (P1~P2For first area R1, P2~P3For Two region R2... ... P6~P7For the 6th region R6), bolted joint is in the 3rd region R3, in measurement process, sample frequency is 1024Hz, a length of 4s during sampling.
(2) the structural response data under 3 kinds of operating modes are measured in the present embodiment, are normal condition, joint portion damage shape respectively State and connector and joint portion while faulted condition.Realize that joint portion is damaged by release bolt pretightning force, spiral shell under normal condition Bolt pretightning force is 24Nm, and bolt pretightening is 7Nm under the faulted condition of joint portion, and connector damage is cantilever beam and free beam Damaging simultaneously, wherein cantilever beam damage occurs at from fixing end 30cm (in second area), as shown in Fig. 3 (b), free beam damage Wound occurs at from fixing end 98cm, i.e., from (in the 5th region), as shown in Fig. 3 (a), passing through sand at free beam perforate end 23cm Turbine respectively cuts out the crack that depth is 10mm in beam both sides, reaches the purpose of injury region Stiffness degradation.
(3) the measuring point response under different operating modes is normalized, calculates auto-correlation coefficient hangover, partial correlation coefficient Truncation, select AR models to carry out data fitting, optimal models exponent number is determined according to BIC criterion, obtains the time sequence of measurement data Row model.The residual sequence between measured data and model of fit is calculated, structural response feature is used as using residual sequence standard deviation.
(4) relation for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, calculates state to be measured Under structural damage sensitive indicator, identification bolted joint damage.
Bolted joint non-destructive tests result is as shown in figure 4, a kind of as can be seen from Figure 4 merge Time-Series analysis and comentropy Bolted joint damnification recognition method, in this specific embodiment only containing joint portion damage situation and in joint portion and company Fitting under degree of impairment, can identify that joint portion is damaged exactly simultaneously.
It is contemplated that by being combined with specific bolted joint structure and further being improved and developed, When a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy of the present invention is in monitoring structural health conditions During the extensive use of field, caused engineering application value will be huge.Simultaneously in structural healthy monitoring system, bolt is added Connect joint portion connection status monitoring modular, can to get the mastery in being converted in engineering technology, produce huge economic benefit and Commercial value.
It is described above, patent preferred embodiment only of the present invention, but the protection domain of patent of the present invention is not limited to This, any one skilled in the art is in the scope disclosed in patent of the present invention, according to the skill of patent of the present invention Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the protection domain of patent of the present invention.

Claims (5)

  1. A kind of 1. bolted joint damnification recognition method for merging Time-Series analysis and comentropy, it is characterised in that methods described bag Include following steps：
    1) arrange that exciting bank is used to give structure white-noise excitation in bolted joint structure, while arrangement is more in structure Individual acceleration transducer is used for surveying the acceleration responsive sequence of structurally corresponding measuring point；
    2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, using standard deviation maximum as normalized parameter, is returned One selects conjunction the characteristics of changing actual measureed value of acceleration response, responded according to actual measureed value of acceleration in AR models, arma modeling and MA models Suitable time series models carry out data fitting；
    3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, is rung by structure of residual sequence standard deviation Answer feature；
    4) relation for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, calculates the knot under state to be measured Structure damage locating index, identify the damage of bolted joint structure.
  2. 2. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 1, its It is characterised by：In step 1), the multiple acceleration transducer is arranged in the both sides of each connector of bolted joint structure.
  3. 3. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 1, its It is characterised by, methods described specifically includes following steps：N number of survey is arranged altogether in each connector both sides of bolted joint structure Point, the acceleration responsive sequence { x that measuring point is corresponded under white-noise excitation is measured by acceleration transduceri, sequence { xiRepresent to survey The n orderly acceleration responsive sequences that point i is gathered under same time separation delta t, the acceleration responsive sequence gathered with N number of measuring point Row initial data maximum standard deviation max (σi) it is normalized parameter, carry out data normalization：
    <mrow> <msub> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;prime;</mo> </msup> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    In formulaIt is measuring point i acceleration responsive sequences { xiAverage,It is measuring point i in t acceleration responsive initial data xi,tValue after normalization, calculate the auto-correlation coefficient and partial correlation coefficient of each measuring point：
    <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mi>k</mi> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;prime;</mo> </msup> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;prime;</mo> </msup> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;prime;</mo> </msup> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> <mo>&amp;ForAll;</mo> <mn>0</mn> <mo>&lt;</mo> <mi>k</mi> <mo>&lt;</mo> <mi>n</mi> </mrow>
    In formulaIt is acceleration responsive values of the measuring point i in t+k time Δts, ρi(k) measuring point i k rank auto-correlation coefficients are represented, Measuring point i k ranks partial correlation coefficient is equal with the value of k-th of autoregressive coefficient of AR (k) models, can estimate in MATLAB tool boxes Obtained after counting AR (k) model parameters of response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, select AR models, Suitable time series models carry out data fitting in arma modeling or MA models：
    In formulaRepresent measuring point i in the acceleration responsive values of t- time Δts, measuring point i in t-2 respectively Acceleration responsive value ... the measuring point i of time Δt is in the acceleration responsive value of t-p time Δts, εt、εt-1……εt-qTable respectively Show the residual error of t, t- time Δts residual error ... t-q time Δts residual error,First is represented respectively Autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnRespectively first is represented to slide back Return coefficient, second slip regression coefficient ..., n-th of slip regression coefficient, subscript p, q represents to include respectively p ranks in model certainly Regression coefficient and q ranks slide regression coefficient；After selecting suitable time series models, complete parameter using MATLAB tool boxes and estimate Meter, during parameter Estimation, first setting models exponent number, using posteriority method, consider fitting degree and independent variable using BIC criterion Number, an optimal models is selected in numerous valid models：
    <mrow> <mi>B</mi> <mi>I</mi> <mi>C</mi> <mo>=</mo> <mi>n</mi> <mi> </mi> <msubsup> <mi>ln&amp;sigma;</mi> <mi>&amp;epsiv;</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <mi>ln</mi> <mi> </mi> <mi>n</mi> <mo>)</mo> </mrow> <mi>m</mi> </mrow>
    N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms state to be measured and base The optimal models of the quasi- each measuring point data of state simultaneously estimates its parameter, calculates each measuring point actual measureed value of acceleration response data and fitting Residual sequence between model：
    Residual sequence using between each measuring point actual measureed value of acceleration response data and model of fit responds as each Measuring Point Structure Feature, introduce the relation that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, the structural damage sensitive indicator of structure The absolute value sum for difference of being itemized for the comentropy of state to be measured and normal condition：
    <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    Ui=-pi log pi
    <mrow> <mi>D</mi> <mi>S</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mrow> <msubsup> <mi>U</mi> <mi>j</mi> <mrow> <mi>t</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>U</mi> <mi>j</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow>
    σ in formulai(ε) and σi+1(ε) represents measuring point i and measuring point i+1 acceleration responsive residual sequence standard deviation, U respectivelyiRepresent by The comentropy subitem value of measuring point i and measuring point i+1 structures, wherein Uj testAnd Uj refThe letter of state and normal condition to be measured is represented respectively Entropy subitem is ceased, DSF (i) represents the damage locating index value calculated by measuring point i and measuring point i+1 acceleration responsive data, if State to be measured carrys out self-structure normal condition, and two adjacent measuring point response residual sequence standard deviations of state and normal condition to be measured are formed Comentropy subitem it is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, bolt combines Portion region DSF (i) changes are much larger than other regional changes, so as to identify that bolted joint is damaged.
  4. 4. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 3, its It is characterised by：If the auto-correlation coefficient hangover of each measuring point, partial correlation coefficient truncation then select AR models；If each measuring point from Coefficient correlation truncation, partial correlation coefficient hangover then select MA models；If the auto-correlation coefficient hangover of each measuring point, partial correlation coefficient Hangover then selects arma modeling.
  5. 5. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 1, its It is characterised by：Methods described is rung using the acceleration of bolted joint structure under Time Series Analysis Model fitting white-noise excitation Data are answered, by introducing the relation between the comentropy quantization two neighboring measuring point of bolted joint structure, with state to be measured and base The absolute value sum of the comentropy subitem difference of quasi- state acceleration responsive is as damage locating index.
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